Solve the Problem $$p ( x ) = 3 ( x + 3 ) ^ { 3 } - 3$$

Solve the problem.
- $$p ( x ) = 3 ( x + 3 ) ^ { 3 } - 3$$
a. Identify the power function of the form $y = x ^ { n }$ that is the parent function to the given graph.
b. In order, outline the transformations that would be required on the graph of $y = x ^ { n }$ to make the graph of the given function.
c. Match the function with the graph.
i.


ii.

iii.


iv.

A) a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Stretch vertically by a factor of 3 . Shift downward 3 units.
c. Graph iii.
B) a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Stretch vertically by a factor of 3 . Shift downward 3 units.
c. Graph ii.
C) a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Stretch vertically by a factor of 3 . Shift downward 3 units.
c. Graph i.
D) a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Shrink vertically by a factor of $\frac { 1 } { 3 }$ . Shift downward 3 units.
c. Graph iv.